Lower Bounds on the Lowest Spectral Gap of Singular Potential Hamiltonians |
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Authors: | Sylwia Kondej Ivan Veselić |
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Institution: | 1.Institute of Physics,University of Zielona Gora,Zielona Gora,Poland;2.Fakult?t für Mathematik,TU Chemnitz and Emmy-Noether-Programme of the DFG,Chemnitz,Germany |
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Abstract: | We analyze Schr?dinger operators whose potential is given by a singular interaction supported on a sub-manifold of the ambient
space. Under the assumption that the operator has at least two eigenvalues below its essential spectrum we derive estimates
on the lowest spectral gap. In the case where the sub-manifold is a finite curve in two dimensional Euclidean space the size
of the gap depends only on the following parameters: the length, diameter and maximal curvature of the curve, a certain parameter
measuring the injectivity of the curve embedding, and a compact sub-interval of the open, negative energy half-axis which
contains the two lowest eigenvalues.
Dedicated to Krešimir Veselić on the occasion of his 65th birthday.
Submitted: February 20, 2006; Accepted: May 8, 2006 |
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Keywords: | |
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